29 Jun '09 05:151 edit

A line of 100 airline passengers is waiting to board a plane. They each hold a ticket to one of the 100 seats on that flight. Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All of the other passengers are quite normal, and will go to their proper seat unless it is already occupied. If it is occupied, they will then find a free seat to sit in, at random. What is the probability that the last person to board the plane will sit in their proper seat?

Will the probability change if you add another person? Why or why not?

Will the probability change if you add another person? Why or why not?